Exploring Links for the Gaussian Distribution

Overview

Compared to the linear model, one advantage of the generalized linear model is its ability to model different relationships between the response variable and the predictors. One challenge is knowing which link to use. In this vignette, we will explore how different relationships affect correlation and the visual appearance of scatter plots.

Summary

We have explored different links for the gaussian distribution, but the gaussian distribution is not a special case. Everything that was done here could be done for any distribution in the glm framework. Once you understand one distribution, you are very far along in understanding the other distributions. The glm framework can handle categorical response variables (binomial), integer response variables (poisson), and right skewed response variables (gamma and inverse gaussion).